You are cordially invited to the Graduate Mathematics Seminar Series organized by the Department of Mathematics.
Speaker: Serkan Doğan (Bilkent University)
“A topological proof of the Abel–Ruffini theorem”
Abstract: The classical Abel–Ruffini theorem states that the general polynomial equation of degree five or higher cannot be solved by radicals. While this result is often approached through Galois theory, this talk presents a different perspective based on topology.
The main idea is to study how the roots of a polynomial change as its coefficients vary continuously along loops in the space of polynomials. By lifting these loops to the space of roots, we obtain permutations of the roots, revealing a connection between the topology of polynomial spaces and the algebraic structure of permutation groups. We will explore how this connection leads to an obstruction to expressing the roots of a general quintic using radicals.
The talk aims to illustrate how topological ideas can address a classical algebraic problem, highlighting the interplay between algebra, geometry, and topology.
Advisor: Asst. Prof. Cihan Okay
Date: November 12, Thursday, 2026
Time: 14:30
Place: SA- 141